Answer
$x = 7$
$y = 7\sqrt 3$
Work Step by Step
The diagram is that of a $30^{\circ}-60^{\circ}-90^{\circ}$ triangle because one angle measures $60^{\circ}$, another measures $90^{\circ}$, and the last angle must measure $30^{\circ}$.
In this type of right triangle, the hypotenuse is two times the shorter leg. Let's write an equation to solve for $x$, the length of the shorter leg:
$14 = 2(x)$
Divide both sides of the equation by $2$ to solve for $x$:
$x = 7$
In this triangle, the longer leg is $\sqrt 3$ times the length of the shorter leg. Since we just found the length of the shorter leg, we can now set up an equation to solve for $y$, the length of the longer leg:
$y = \sqrt 3(7)$
Rewrite the radical in a more standard form:
$y = 7\sqrt 3$
